In this talk I will provide an overview of some of the work we do when it comes to solving inference
problems in nonlinear dynamical systems. A proper subtitle for the talk is “strategies and
examples”, since I will only provide solution strategies and show that these strategies can
successfully solve challenging applications. The first topic is parameter inference problems in
nonlinear dynamical systems (a.k.a. nonlinear system identification). The maximum likelihood problem
is solved using a combination of the expectation maximization (EM) algorithm and sequential Monte
Carlo (SMC) methods (e.g., the particle filter and the particle smoother). The Bayesian problem is
solved using a combination of Markov chain Monte Carlo (MCMC) and SMC . As an example, we show how to
estimate a particular special case known as the Wiener model (a linear dynamical model followed by a
static nonlinearity). The second topic is that of sensor fusion, which refers to the problem of
inferring states (and possibly parameters) using measurements from several different, often
complementary, sensors. The strategy is explained and (perhaps more importantly) illustrated using
three of the industrial applications we are working with; 1. Navigation of fighter aircraft (using
inertial sensors, radar and maps); 2. Indoor positioning of humans (using inertial sensors and
maps); 3. Indoor pose estimation of a human body (using inertial sensors and ultra-wideband).